Skip to main content

Multidimensional Permutation Entropy for Constrained Motif Discovery

  • Conference paper
  • First Online:
Intelligent Information and Database Systems (ACIIDS 2019)

Abstract

Constrained motif discovery was proposed as an unsupervised method for efficiently discovering interesting recurrent patterns in time-series. The de-facto standard way to calculate the required constraint on motif occurrence locations is change point discovery. This paper proposes the use of time-series complexity for finding the constraint and shows that the proposed approach can achieve higher accuracy in localizing motif occurrences and approximately the same accuracy for discovering different motifs at three times the speed of change point discovery. Moreover, the paper proposes a new extension of the permutation entropy for estimating time-series complexity to multi-dimensional time-series and shows that the proposed extension outperforms the state-of-the-art multi-dimensional permutation entropy approach both in speed and usability as a motif discovery constraint.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Bandt, C., Pompe, B.: Permutation entropy: a natural complexity measure for time series. Phys. Rev. Lett. 88(17), 174102 (2002). https://doi.org/10.1103/PhysRevLett.88.174102

    Article  Google Scholar 

  2. Catalano, J., Armstrong, T., Oates, T.: Discovering patterns in real-valued time series. In: Fürnkranz, J., Scheffer, T., Spiliopoulou, M. (eds.) PKDD 2006. LNCS (LNAI), vol. 4213, pp. 462–469. Springer, Heidelberg (2006). https://doi.org/10.1007/11871637_44

    Chapter  Google Scholar 

  3. Chavarriaga, R., et al.: The opportunity challenge: a benchmark database for on-body sensor-based activity recognition. Pattern Recogn. Lett. 34(15), 2033–2042 (2013). https://doi.org/10.1016/j.patrec.2012.12.014

    Article  Google Scholar 

  4. Chiu, B., Keogh, E., Lonardi, S.: Probabilistic discovery of time series motifs. In: 9th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD 2003, pp. 493–498. ACM, New York (2003).https://doi.org/10.1145/956750.956808

  5. He, S., Sun, K., Wang, H.: Multivariate permutation entropy and its application for complexity analysis of chaotic systems. Phys. A Stat. Mech. Appl. 461, 812–823 (2016)

    Article  MathSciNet  Google Scholar 

  6. Lin, J., Keogh, E., Wei, L., Lonardi, S.: Experiencing sax: a novel symbolic representation of time series. Data Min. Knowl. Disc. 15(2), 107–144 (2007)

    Article  MathSciNet  Google Scholar 

  7. Mohammad, Y., Nishida, T.: Learning interaction protocols using augmented Baysian networks applied to guided navigation. In: IEEE/RSJ International Conference on Intelligent Robots and Systems, IROS 2010, pp. 4119–4126. IEEE, October 2010. https://doi.org/10.1109/IROS.2010.5651719

  8. Mohammad, Y., Ohmoto, Y., Nishida, T.: G-SteX: greedy stem extension for free-length constrained motif discovery. In: Jiang, H., Ding, W., Ali, M., Wu, X. (eds.) IEA/AIE 2012. LNCS (LNAI), vol. 7345, pp. 417–426. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-31087-4_44

    Chapter  Google Scholar 

  9. Mohammad, Y., Nishida, T.: Constrained motif discovery in time series. New Gener. Comput. 27(4), 319–346 (2009)

    Article  Google Scholar 

  10. Mohammad, Y., Nishida, T.: On comparing SSA-based change point discovery algorithms. In: IEEE/SICE International Symposium on System Integration, SII 2011, pp. 938–945 (2011)

    Google Scholar 

  11. Mohammad, Y., Nishida, T.: Exact discovery of length-range motifs. In: Nguyen, N.T., Attachoo, B., Trawiński, B., Somboonviwat, K. (eds.) ACIIDS 2014. LNCS (LNAI), vol. 8398, pp. 23–32. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-05458-2_3

    Chapter  Google Scholar 

  12. Mohammad, Y., Nishida, T.: Scale invariant multi-length motif discovery. In: Ali, M., Pan, J.-S., Chen, S.-M., Horng, M.-F. (eds.) IEA/AIE 2014. LNCS (LNAI), vol. 8482, pp. 417–426. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-07467-2_44

    Chapter  Google Scholar 

  13. Mohammad, Y., Nishida, T.: Exact multi-length scale and mean invariant motif discovery. Appl. Intell. 44, 1–18 (2015)

    Google Scholar 

  14. Mohammad, Y., Nishida, T.: Shift density estimation based approximately recurring motif discovery. Appl. Intell. 42(1), 112–134 (2015)

    Article  Google Scholar 

  15. Mohammad, Y., Nishida, T.: \(MC^2\): an integrated toolbox for change, causality and motif discovery. In: Fujita, H., Ali, M., Selamat, A., Sasaki, J., Kurematsu, M. (eds.) IEA/AIE 2016. LNCS (LNAI), vol. 9799, pp. 128–141. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-42007-3_12

    Chapter  Google Scholar 

  16. Mohammad, Y., Nishida, T.: Unsupervised discovery of basic human actions from activity recording datasets. In: IEEE/SICE International Symposium on System Integration, SII 2012, pp. 402–409. IEEE (2012)

    Google Scholar 

  17. Mohammad, Y., Ohmoto, Y., Nishida, T.: CPMD: a matlab toolbox for change point and constrained motif discovery. In: Jiang, H., Ding, W., Ali, M., Wu, X. (eds.) IEA/AIE 2012. LNCS (LNAI), vol. 7345, pp. 114–123. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-31087-4_13

    Chapter  Google Scholar 

  18. Morabito, F.C., Labate, D., Foresta, F.L., Bramanti, A., Morabito, G., Palamara, I.: Multivariate multi-scale permutation entropy for complexity analysis of Alzheimer’s disease EEG. Entropy 14(7), 1186–1202 (2012)

    Article  Google Scholar 

  19. Mueen, A.: Enumeration of time series motifs of all lengths. In: 2013 IEEE 13th International Conference on Data Mining (ICDM). IEEE (2013)

    Google Scholar 

  20. Mueen, A., Keogh, E., Zhu, Q., Cash, S., Westover, B.: Exact discovery of time series motifs. In: SIAM International Conference on Data Mining, SDM 2009, pp. 473–484 (2009)

    Google Scholar 

  21. Riedl, M., Müller, A., Wessel, N.: Practical considerations of permutation entropy. Eur. Phys. J. Spec. Top. 222(2), 249–262 (2013)

    Article  Google Scholar 

  22. Tanaka, Y., Iwamoto, K., Uehara, K.: Discovery of time-series motif from multi-dimensional data based on MDL principle. Mach. Learn. 58(2/3), 269–300 (2005)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding authors

Correspondence to Yomna Rayan or Yasser Mohammad .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Rayan, Y., Mohammad, Y., Ali, S.A. (2019). Multidimensional Permutation Entropy for Constrained Motif Discovery. In: Nguyen, N., Gaol, F., Hong, TP., Trawiński, B. (eds) Intelligent Information and Database Systems. ACIIDS 2019. Lecture Notes in Computer Science(), vol 11431. Springer, Cham. https://doi.org/10.1007/978-3-030-14799-0_20

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-14799-0_20

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-14798-3

  • Online ISBN: 978-3-030-14799-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics